The main purpose of borehole sonic logging is to provide an estimate of the formation slowness. If a monopole source is excited in the borehole, it is possible to obtain the compressional and shear slowness of fast and intermediate formations, in which the rock slowness is less than the borehole fluid slowness. A standard method of extracting the compressional slowness is to use the standard coherence approach. C. V. Kimball and T. L. Marzetta, Semblance processing of borehole acoustic array data, GEOPHYSICS vol. 49, no. 3, pp. 274-281 (1984). In slow formations, when the shear slowness is greater than that of the fluid, the dipole source is used and measurement of the dipole flexural mode allows the estimation of the shear slowness of the formation. In this case, semblance processing is still applied, but it integrates the dispersive behavior of the dipole flexural mode. C. V. Kimball, Shear slowness measurement by dispersive processing of the borehole flexural mode, GEOPHYSICS vol. 63, no. 2, pp. 337-344 (1996).
Until now, the main outputs extracted from waveforms recorded by a high-frequency monopole source were the compressional slowness of the formation and sometimes the shear depending on the formation (fast and intermediate formations). Nevertheless, the development of new complex fields, where wellbore stability and optimal well completion are of key importance, requires more information than the traditional standard log curves provide. One of the current main interests is in acquiring the radial formation slowness profile of a formation from shallow to deep. For example, a completion engineer is interested to learn of the possible existence of an altered zone around the well that may have a bearing on perforation design, and a geophysicist may want to know the measurement of the far compressional slowness beyond the altered formation. To provide this information, it is necessary to provide compressional and shear slowness profiles as a function of the radial distance into the formation.
In the monopole case, the ability to record such information is strongly related to the characteristics of the tool that will record the data. In fact, the depth of penetration into the formation is a function of the distance between the transmitter and the first receiver in the array, the frequency content of the emitted signal, and the array aperture. Therefore, to accommodate various depths of investigation of the emitted signal, a tool may contain multiple transmitters located at various source-to-receiver (TR) spacings combined with a sufficiently large array aperture.
In 1993, Hornby (B. Hornby, Tomographic reconstruction of near-borehole slowness using refracted borehole sonic arrivals, GEOPHYSICS vol. 58, pp. 1726-1738 (1993)) presented a method for reconstructing a 2D map of near-borehole slowness by inverting the first arrival time of compressional head waves by using the simultaneous iterative reconstruction technique (SIRT). K. A. Dynes and R. J. Lytle, Computerized geophysical tomography, PROC. INST. ELECT. AND ELECTROM. ENG., vol. 67, pp. 1065-1073 (1979). This proposed inversion technique has been found to be quite sensitive with respect to the choice of the initial slowness model needed to start the inversion and also with respect to mud slowness and borehole diameter.
Accordingly, some aspects of the present invention relate to methods and apparatus for estimating a 2D (axial and radial) or 3D image of the formation compressional or shear slowness, in real time and with minimal user interaction. The inversion scheme may be based on a simple analytical expression linking the estimated transit time to the slowness variation around the wellbore. This simple formulation of the problem may enable fast and easy inversion making this product suitable for well site implementation. The methods and apparatus may invert for a varying profile when the slowness decreases monotonically with radial distance in the formation. The methods and apparatus described herein may not be sensitive to the mud, borehole diameter, and initial background slowness. Selected examples of data recorded with a new wireline tool suitable for compressional tomography analysis are presented to demonstrate the robustness and reliability of the proposed radial profiling technique.